Fundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Sense

Teodoro, A. Di; Ferreira, M.; Vieira, N.

http://hdl.handle.net/10400.8/14212

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Fundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Sense.pdf	In this paper, we study the fundamental solution of natural powers of the n-parameter fractional Laplace and Dirac operators defined via Riemann–Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace Δa+α and Dirac Da+α operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag–Leffler function.	434.9 KB	Adobe PDF	Download

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Authors

Teodoro, A. Di

Ferreira, M.

Vieira, N.

Abstract(s)

In this paper, we study the fundamental solution of natural powers of the n-parameter fractional Laplace and Dirac operators defined via Riemann–Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace Δa+α and Dirac Da+α operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag–Leffler function.

Keywords

Fractional Clifford analysis Fractional derivatives Fundamental solution Poisson’s equation Laplace transform

URI

http://hdl.handle.net/10400.8/14212

Citation

Teodoro, A.D., Ferreira, M. & Vieira, N. Fundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Sense. Adv. Appl. Clifford Algebras 30, 3 (2020). https://doi.org/10.1007/s00006-019-1029-1.